Question

A table is shown with two rows and two columns. The horizontal side is labeled negative 4 x superscript 4 baseline and 10 x while the vertical side is labeled 5 x cubed and negative 1.
Find the product when you multiply the polynomials (−4x4+10x)(5x3−1) .

(1 point)
Responses

−20x7+50x4−6x
negative 20 x superscript 7 baseline plus 50 x superscript 4 baseline minus 6 x

−20x7−54x4−10x
negative 20 x superscript 7 baseline minus 54 x superscript 4 baseline minus 10 x

−20x7+54x4−10x
negative 20 x superscript 7 baseline plus 54 x superscript 4 baseline minus 10 x

20x7+54x4−10x
20 x superscript 7 baseline plus 54 x superscript 4 baseline minus 10 x
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Answer 1

To find the product of the polynomials \((-4x^4 + 10x)(5x^3 - 1)\), we can use the distributive property (also known as the FOIL method for binomials).

1. Multiply each term in the first polynomial by each term in the second polynomial:

\[
(-4x^4)(5x^3) + (-4x^4)(-1) + (10x)(5x^3) + (10x)(-1)
\]

2. Now, perform the multiplications:

- First term: \((-4x^4)(5x^3) = -20x^7\)
- Second term: \((-4x^4)(-1) = 4x^4\)
- Third term: \((10x)(5x^3) = 50x^4\)
- Fourth term: \((10x)(-1) = -10x\)

3. Now, add all the terms together:

\[
-20x^7 + 4x^4 + 50x^4 - 10x
\]

4. Combine like terms:

- The \(x^4\) terms: \(4x^4 + 50x^4 = 54x^4\)

So, the final expression becomes:

\[
-20x^7 + 54x^4 - 10x
\]

The correct answer is:

\(-20x^7 + 54x^4 - 10x\) (which matches the third response option).